Differential photometry — method and equations¶

This page states exactly what ARGOS computes, with the equations as they are implemented. Every formula below is traceable to a module in argos.core.photometry; the API reference gives the signatures.

Scope

ARGOS measures raw, uncalibrated sub-exposures. No dark, flat or bias is applied, and no colour transformation to a standard photometric system is performed. The result is a quick-look light curve: enough to see that a variable is varying, that comparison stars are stable and that the night is usable — not a publishable measurement. Calibration, registration and final photometry belong to Siril and star_var_script, on the raw frames ARGOS preserves.

1. The measurement grid: the green plane¶

Every geometric and photometric quantity is defined on one grid, so a pixel in the astrometric solution is the same pixel that is measured.

The sensor is a colour (CFA) detector with a GRBG Bayer pattern. ARGOS forms the green plane as the per-tile average of the two green samples:

\[ G(i, j) = \tfrac{1}{2}\left[\,\text{raw}(2i,\,2j) + \text{raw}(2i{+}1,\,2j{+}1)\,\right] \]

The plane has shape \((H/2,\ W/2)\); odd dimensions are cropped by one row or column so the two greens line up. Green is used because it is the densest sampling of the Bayer mosaic and therefore the best signal-to-noise channel for stars.

Note

One green pixel spans two raw pixels. The plate solver reports its scale per green pixel; ARGOS converts that to the full-resolution scale before showing it in the interface, so the two never disagree on screen. It is not written to the FITS file: the saved frames carry no WCS and no plate-scale keyword at all (see FITS headers reference).

Averaging the two greens is not free. It broadens the effective PSF by up to half a green pixel — about 3.7″ on an S30 Pro — and it bakes in any G1/G2 response imbalance, a common CMOS artefact. Both are accepted in exchange for \(\sqrt{2}\) in signal-to-noise and a grid that lines up exactly with the astrometric solution.

Two consequences matter scientifically:

The green plane is not a photometric \(V\) band. It is an instrumental passband, recorded as TG — the AAVSO code for an untransformed green channel, defined in the DSLR Observing Manual. Do not report it as \(V\).
Interpolated debayering is never used for measurement. Debayer mode, stretch and channel selection are display settings; the data pipeline reads the CFA array.

2. Astrometry: from pixels to sky¶

Plate solving is delegated to ASTAP, which solves the green plane and returns a WCS. The WCS is what makes identification possible: catalogue positions (Gaia DR3, AAVSO VSX, SIMBAD, the NASA Exoplanet Archive, AAVSO VSP) are projected into pixel coordinates, and a click on a star is projected back to \((\alpha, \delta)\).

This is astrometric only. ARGOS does not perform differential astrometry in the sense of measuring proper motion or parallax; the solution exists to answer “which star is this?” and “where is my aperture?”, frame after frame.

Because the field rotates on an alt-azimuth mount, apertures are re-derived from the WCS on each solved frame rather than held at fixed pixel coordinates.

3. Aperture photometry¶

Implemented in argos.core.photometry.aperture.

3.1 Geometry¶

The aperture radius adapts to the seeing measured on the frame:

\[ r_\text{ap} = \max\left(r_\text{min},\ k \cdot \text{FWHM}\right) \]

with \(k = 2.5\) and \(r_\text{min} = 4\) green px by default. The sky annulus has default radii \(r_\text{in} = 8\) and \(r_\text{out} = 12\) green px, constrained so that the annulus never touches the aperture:

\[ r_\text{in} \ge r_\text{ap} + 1, \qquad r_\text{out} \ge r_\text{in} + 2 \]

When a frame carries no measured FWHM — re-measuring a saved sub, for instance — a fallback FWHM of 3.0 green px is used. Note what that gives: \(\max(4,\ 2.5 \times 3.0) = 7.5\) px. It does not fall back to \(r_\text{min}\).

Warning

The live run and an offline re-measurement are not the same measurement. Live frames carry a measured FWHM, so the aperture is typically at or near the 4 px floor. A re-measurement of saved subs has no FWHM and uses 7.5 px — 1.9× the radius, 3.5× the area, with correspondingly more sky and more neighbours. Do not overlay a live curve and a re-measured one and read the difference as astrophysics.

Aperture size on the sky¶

The radii above are in green-plane pixels, each spanning two raw pixels. In angular terms, for the shipped profiles:

Profile	″ / green px	\(r_\text{ap}\) = 4 px	fallback 7.5 px	annulus 8–12 px
S30 Pro (160 mm)	7.48	29.9″	56.1″	60–90″
S30 (150 mm)	7.98	31.9″	59.8″	64–96″
S50 (250 mm)	4.79	19.1″	35.9″	38–57″

A 30-arcsecond aperture is enormous — check for neighbours

This is the error source least visible on screen and most likely to ruin a curve. At 30″ radius, any field within ~20° of the galactic plane will put a second star inside somebody’s aperture, and several inside the sky annulus.

A blended companion is mostly harmless while the seeing is constant: it adds a fixed offset that differential photometry absorbs. It stops being harmless the moment the FWHM changes, because the fraction of the companion’s light inside the aperture then changes too — producing a variation correlated with seeing that looks exactly like astrophysics. If your target’s brightness tracks the FWHM trend in the Metrics tab, suspect a blend before you suspect the star.

Before assigning a role, zoom in and look at the aperture circle.

Why 2.5 × FWHM? It is not the signal-to-noise optimum, which sits nearer 1×FWHM (Howell 1989; optimal extraction in Naylor 1998). A wide aperture is chosen deliberately: it captures essentially all of the flux, so the measurement is insensitive to seeing-dependent aperture losses — which is what matters when you are differencing frames taken over hours. The price is sky noise and blending, paid knowingly.

3.2 Sky and flux¶

The sky level \(\tilde{s}\) is the median of the annulus pixels, not the mean: a median is insensitive to a star that happens to fall in the annulus. With \(n_\text{pix}\) pixels inside the aperture,

\[ F = \sum_{(i,j)\,\in\,\text{ap}} I(i,j) \;-\; n_\text{pix}\,\tilde{s} \]

in ADU.

3.3 Noise¶

The uncertainty is the CCD equation, evaluated in electrons through the gain \(g\) (e⁻/ADU). With \(F_e = g F\), \(s_e = g\tilde{s}\) and read noise \(R\) (e⁻ RMS, default 1.5):

\[ \sigma_F^2 = F_e + n_\text{pix}\left(s_e + R^2\right) \]

The three terms are the star’s own photon noise, the sky photon noise and the read noise, each summed over the aperture. The signal-to-noise ratio is \(\text{SNR} = F_e / \sigma_F\).

Source — the CCD equation

Merline & Howell (1995); Howell, Handbook of CCD Astronomy (2006). Full citations in References and further reading.

Three terms of the textbook equation are absent.

The uncertainty of the sky estimate itself. The published equation carries a factor \(\left(1 + n_\text{pix}/n_\text{ann}\right)\) on the background terms, because \(\tilde{s}\) is measured from a finite annulus and its own error propagates into every aperture pixel. ARGOS omits it. Because the sky is a median rather than a mean, the correct factor is closer to \(1 + \tfrac{\pi}{2}\,n_\text{pix}/n_\text{ann}\). With the shipped geometry that is about 1.3 for a live frame at \(r_\text{ap} = 4\), and about 2.3 for the 7.5 px fallback — so the sky-plus-read variance is understated by 30 % live, and by more than a factor of two on a re-measurement.

Dark current is never measured: its signal is absorbed into the annulus median and subtracted with the sky, but its shot noise is not counted — small on short uncooled sub-exposures against a bright sky, and larger if you observe cold and dark.

Digitisation noise is negligible next to a 1.5 e⁻ read noise.

All three would have to be restored for a calibrated reduction. The first is the one that matters most here, and it means \(\sigma_F\) is an underestimate — which is part of why the run-level floor of §5 exists.

Where does \(g\) come from — and when is it wrong?

During a live run ARGOS resolves the electron gain in order: the camera.egain_table entry for the current gain setting, else the driver’s ElectronsPerADU, else the sensor reference curve for the profile’s sensor. That value is what goes into EGAIN in the FITS header.

An offline re-measurement of saved subs does not do this. It reads camera.egain_table only, and that table is empty by default — in which case \(g\) falls back to 1.0 and ADU are treated as electrons. Every SNR from a batch re-measurement is then wrong, and every \(\sigma_m\) with it. If you re-measure, populate camera.egain_table first.

The read noise is one number for three sensors

photometry.read_noise_e is a single configured constant, 1.5 e⁻ by default. The RDNOISE value ARGOS writes into the same frame’s header is looked up per sensor and per gain, and ranges from about 0.5 to 6.9 e⁻ across the shipped profiles. The default matches no supported sensor at a typical gain. For sky-limited exposures this barely moves \(\sigma_F\); for short or dark-sky frames it does. Set it from the sensor reference for your gain if the read term is not negligible.

3.4 Instrumental magnitude¶

\[ m_\text{inst} = -2.5 \log_{10} F \]

undefined for \(F \le 0\), which is reported as a missing measurement rather than silently clamped. Its uncertainty follows from differentiating the logarithm:

\[ \sigma_{m} = \frac{2.5}{\ln 10}\cdot\frac{\sigma_F}{F_e} \simeq 1.0857\,\frac{\sigma_F}{F_e} \]

3.5 Two flags, and exactly what they do¶

Saturation. Any aperture pixel at or above camera.linearity_max_adu (50 000 ADU by default) flags the measurement.

The 50 000 ADU default is not reconciled with the sensor tables

ARGOS writes both EGAIN (e⁻/ADU) and FULLWELL (e⁻) into every frame from its own sensor references. Those three numbers ought to satisfy \(\text{EGAIN} \times \texttt{linearity\_max\_adu} \le \text{FULLWELL}\). They do not, at any shipped gain:

Sensor	Gain	EGAIN	FULLWELL	Well fills at
IMX585 (S30 Pro)	0	3.00	38 000 e⁻	12 700 ADU
IMX585 (S30 Pro)	100	1.50	38 000 e⁻	25 300 ADU
IMX662 (S30)	0	6.00	38 200 e⁻	6 400 ADU
IMX462 (S50)	80	1.10	11 200 e⁻	10 200 ADU

Read literally, the flag fires after the well is already full — which means it does not protect you. The likely cause is a unit mismatch: the sensor is a 12-bit ADC whose output is scaled into a 16-bit file, and it is not recorded anywhere whether EGAIN is referenced to a stored 16-bit ADU or to an ADC count. Until that is resolved, do not treat 50 000 ADU as a physical linearity limit, and judge saturation from the peak ADU shown on the star card against your own bias/flat experience instead. This is an open defect, recorded here rather than papered over.

A second limitation: saturation is tested on the averaged green plane \((G_1{+}G_2)/2\), so a star that saturates one green sample but not the other can average below the threshold and escape the flag.

Missing PSF support. A real star spreads over neighbouring pixels; a hot pixel or a cosmic-ray hit does not. When the brightest aperture pixel exceeds the sky by more than \(10\sigma_\text{sky}\) while its four neighbours average less than 10 % of that excess, the point is marked suspect. Since the live curve measures raw subs, an uncorrected hot pixel drifting through an aperture would otherwise paint a convincing artificial dip with nothing to point at.

(\(\sigma_\text{sky}\) here is the annulus standard deviation, while the sky level is its median. A star sitting in the annulus inflates that σ and makes the test fire less often — the threshold is more conservative than it looks.)

What the flags actually gate — read this before trusting them

Neither flag removes a bad point from your target’s curve. Both are recorded; only some of them act.

	saturated	suspect
Excludes a comparison from the magnitude zero point	yes	no
Excludes a comparison from the relative-flux sum	yes	yes
Excludes it from automatic selection and from tracking anchors	yes	yes
Removes a flagged target point from the curve	no	no
Appears as a column in `photometry.csv`	yes	no

So: a comparison star flagged only as suspect still contributes to the magnitude ensemble; and a suspect target point is measured, plotted, exported and invisible in the export. Judge suspect points from the live view, before you leave the field.

4. The comparison ensemble¶

Implemented in argos.core.photometry.differential.

4.1 Zero point¶

Each comparison star contributes the difference between its catalogue magnitude and its instrumental magnitude. The zero point is their mean:

\[ \text{ZP} = \frac{1}{n}\sum_{k=1}^{n}\left(m_{\text{cat},k} - m_{\text{inst},k}\right) \]

and the ensemble scatter about it is the sample RMS

\[ \sigma_\text{ZP} = \sqrt{\frac{1}{n-1}\sum_{k=1}^{n}\left(d_k - \text{ZP}\right)^2}, \qquad d_k = m_{\text{cat},k} - m_{\text{inst},k} \]

With a single comparison this expression has no \(n-1\) to divide by. The code reports \(\sigma_\text{ZP} = 0\) — but the scatter is undefined, not zero, and the distinction is the entire point: the ensemble term then vanishes from \(\sigma_\text{formal}\), so the worst possible ensemble produces the smallest error bar. Never read a one-comparison error bar as a measurement of anything.

With two to five comparisons the situation is better but not good: a sample RMS on \(n = 3\) is itself uncertain by roughly 50 %, and \(\sigma_\text{ZP}/\sqrt{n}\) inherits that. This is a second reason the run-level floor of §5 exists.

The zero point is cross-band, by construction

There is no TG catalogue magnitude. AAVSO VSP sequences publish B, V, Rc and Ic; ARGOS measures an untransformed green instrumental magnitude. So when the band requested (photometry.default_band, TG by default) is not in the sequence, the code falls back to V, and every zero point is

\[ \text{ZP} = \operatorname{mean}\left(V_\text{cat} - \text{TG}_\text{inst}\right) \]

This is the accepted practice for untransformed green photometry — it is what TG means, and it is why the AAVSO defines the code. But it makes a colour term the dominant systematic of the whole method, and it is not optional or occasional: it is on every frame.

The practical consequence. Any difference in colour between your target and your ensemble propagates straight into the differential magnitude, and its size changes with airmass — so a red target against a blue ensemble drifts through the night in a way that looks like variability. VSP publishes B and V for every sequence star, so you can compute \(B-V\): match the ensemble’s mean colour to the target within roughly 0.3 mag in \(B-V\) and this mostly goes away. ARGOS does not do this for you, and does not warn you.

Note

The idea of an ensemble zero point rather than a single comparison is Honeycutt’s (1992). ARGOS does not implement his method: Honeycutt solves one global least-squares system across a whole inhomogeneous set of exposures, while ARGOS forms a clipped mean independently on each frame — which is what a live preview can do, frame by frame, with no knowledge of the frames still to come.

4.2 Robust rejection¶

With three or more comparisons, outliers are clipped against the median and the MAD, not the mean and the RMS: in a small ensemble a single bad comparison inflates the RMS enough to hide inside it. A pair is rejected when

\[ \left|d_k - \operatorname{med}(d)\right| \;>\; \max\left(2.5 \times 1.4826\,\operatorname{MAD}(d),\ 0.01\ \text{mag}\right) \]

The factor 1.4826 converts the MAD to a Gaussian-equivalent standard deviation (Rousseeuw & Croux 1993). The 10 mmag floor matters: with three or four near-identical comparisons the MAD can approach zero, and photon noise alone must not be allowed to reject a perfectly good star. At most two iterations run, and clipping stops if fewer than two pairs would remain.

4.3 Differential magnitude¶

\[ m = m_{\text{inst,target}} + \text{ZP} \]

with the formal uncertainty combining the target’s own photon error and the standard error of the ensemble:

\[ \sigma_\text{formal} = \sqrt{\sigma_{m,\text{target}}^{2} + \frac{\sigma_\text{ZP}^{2}}{n}} \]

Fewer than photometry.min_comparisons (2 by default) kept comparisons does not suppress the measurement; it annotates it. A curve built on one comparison star is still shown, and still labelled as such.

4.4 Relative flux, for transits¶

A transit needs no catalogue magnitudes — only a stable ratio. ARGOS therefore also computes

\[ \rho = \frac{F_\text{target}}{\sum_k F_{\text{comp},k}} \]

against the sum of the comparison fluxes, which has the correct ratio statistics. Propagating fractional errors,

\[ \frac{\sigma_\rho}{\rho} = \sqrt{ \left(\frac{1}{\text{SNR}_\text{target}}\right)^{2} + \frac{\sum_k \left(F_k/\text{SNR}_k\right)^{2}}{\left(\sum_k F_k\right)^{2}} } \]

Important

Two different weightings are in play, and they are not equivalent. The zero point of §4.1 is an unweighted mean of magnitude differences — a comparison two magnitudes fainter counts exactly as much as the brightest one. The ratio \(\rho\) is a sum of fluxes, which is the photon-optimal weighting. The flux sum is the statistically better estimator; the magnitude mean is kept because it is what produces a calibrated magnitude against catalogue values. If the two paths disagree on a night, the flux ratio is the one to believe about shape.

\(\rho\) as computed is deliberately not normalised to an out-of-transit baseline and not detrended: both are post-processing decisions that depend on the baseline you actually observed.

Warning

The Relative flux display in the transit panel does normalise — to the median of the series currently shown. That is a display convenience and it has a failure mode: if most of your run is in transit, the median sits inside the event, the baseline is pulled down and the depth looks shallower than it is. Judge depth from an exported, un-normalised series with a real out-of-transit baseline.

4.5 Automatic selection¶

When a target is chosen and the ensemble is still empty, ARGOS proposes up to five comparisons from the AAVSO VSP sequence. Each candidate is measured on a pilot frame and must pass every gate:

not saturated, and not flagged suspect by the PSF-support test of §3.5;
SNR \(\ge 10\) on that pilot frame;
instrumental magnitude within 1.5 mag of the target’s — measured on the same frame, not compared through catalogue magnitudes, so the gate is about landing in the same part of the detector’s response;
separation under 25 arcmin.

The separation limit is deliberate — across a very wide raw field, remote references are vulnerable to flat-field residuals and differential tracking error, and a small validated ensemble beats a large scattered one.

Candidates that clear every gate are then ranked, and the ranking is not what the gates suggest:

\[ \text{score} = 0.50\,S_\text{SNR} + 0.40\,S_{\Delta m} + 0.10\,S_\text{dist} \]

with \(S_\text{SNR} = \min(\text{SNR}/\max(20, 2\,\text{SNR}_\text{min}), 1)\), \(S_{\Delta m} = 1 - \Delta m_\text{inst}/\Delta m_\text{max}\) and \(S_\text{dist} = 1 - \theta/120'\). Because that last term is normalised over 120′ while the hard cut is at 25′, distance contributes at most 0.02 of the final score inside the allowed region — proximity is essentially not a criterion. Signal-to-noise and brightness match are. If a pilot measurement is unavailable the code falls back to nearest-first instead.

A manually clicked star is never replaced by this proposal. It is kept, but because it has no AUID and no catalogue magnitude it cannot contribute a zero point, so ARGOS complements it rather than leaving the target unusable.

5. The run-level systematic floor¶

Implemented in argos.core.photometry.uncertainty. This is the part that makes the error bars honest.

The formal error of §3.4 counts photons, and — per §3.3 — undercounts even those. It does not count scintillation, guiding jitter, aperture losses, flat-field residuals, differential extinction or focus drift, which for a bright star through a small aperture are usually the dominant terms. Left alone, the curve would carry error bars several times too small.

ARGOS measures the real scatter instead of assuming it, using second differences. For independent errors,

\[ \operatorname{Var}\left(m_{i-1} - 2m_i + m_{i+1}\right) = 6\,\sigma^{2} \]

so a robust estimate of the per-point scatter is

\[ \sigma_\text{real} = \frac{1.4826\,\operatorname{MAD}\left(m_{i-1} - 2m_i + m_{i+1}\right)}{\sqrt{6}} \]

The second difference is what makes this work on a variable star: it removes any locally linear trend, so the intrinsic variation of the target does not inflate the noise estimate. Estimating a variance from successive differences rather than from residuals about a fitted model goes back to von Neumann (1941).

What this estimator can and cannot see

Differencing is a high-pass filter, and that cuts both ways. A component varying on a timescale \(T\) much longer than the cadence \(\Delta t\) is suppressed by roughly \((\Delta t / T)^2\) — which is exactly why the target’s own variability does not contaminate it, and exactly why it cannot measure the slow systematics listed above.

Captured: scintillation (white above ~1 s), frame-to-frame guiding jitter, aperture-loss noise, photon noise — everything varying frame to frame.
Not captured: flat-field residuals as the field rotates, differential extinction, colour × airmass, focus drift — everything varying over the night.

\(\sigma_\text{real}\) is therefore a high-frequency scatter, and \(\sigma_\text{sys}\) is the white excess over the formal error, not a measurement of “scintillation plus flat-field plus tracking”. For anything you measure over a long baseline — a transit depth above all — the relevant uncertainty is set by correlated red noise on that timescale, which this number does not contain and will underestimate. Bin your residuals and watch whether the RMS falls as \(1/\sqrt{N}\); where it stops falling is your real floor (Pont, Zucker & Queloz 2006).

And because it comes from a MAD on 10–30 points, \(\sigma_\text{real}\) is itself uncertain at the ±20–30 % level.

The systematic term is what the observed scatter has in excess of the formal errors, and the final uncertainty adds it in quadrature:

\[ \sigma_\text{sys} = \sqrt{\max\left(0,\ \sigma_\text{real}^{2} - \operatorname{med}(\sigma_\text{formal})^{2}\right)}, \qquad \sigma_\text{final} = \sqrt{\sigma_\text{formal}^{2} + \sigma_\text{sys}^{2}} \]

Each point keeps its own formal error, so a genuinely noisy frame stays noisier than its neighbours; the floor is a run-level addition, not a replacement.

At least ten valid measurements are needed for the automatic estimate. Below that, the floor is either taken from the explicit configuration value or omitted entirely, and the curve shows formal errors only.

One uncertainty contract

This is the same robust systematic-floor method used by star_var_script. The live preview and the final reduction therefore quote uncertainties computed the same way, which is what makes them comparable at all.

6. Is the ensemble any good? The leave-one-out check¶

Implemented in argos.core.photometry.quality.

A bad reference star poisons every point of the night, and it does so silently: the target curve simply moves. ARGOS therefore assesses each comparison against the others, without changing anything the observer selected.

The insight is that the work is already done. Every comparison star is itself measured differentially against the other comparisons — a leave-one-out curve. If that curve is not flat, something in the ensemble is wrong.

Warning

The test detects, it does not localise — not with the ensemble sizes ARGOS works with. With three to five comparisons, one bad star sits in the reference set of every other star’s leave-one-out curve, so it makes all of them wander. A single red flag usually means “this ensemble has a problem”, not “this star is the problem”. Localisation needs an ensemble large enough that each leave-one-out subset is still dominated by good stars.

What to do with a flagged ensemble: drop the worst offender, let the assessment re-run, and see whether the others go quiet. If they do, you found it.

For each comparison, over its valid points (not saturated, with finite time, magnitude and error), ARGOS computes the second-difference scatter \(\sigma_\text{real}\) of §5 and the median formal error, then classifies:

Status	Condition
insufficient data	fewer than 10 valid points, or no scatter estimate
Noisy	median formal error \(> 0.10\) mag — the star is too faint or too poorly measured to judge
Unstable	scatter \(> 0.10\) mag — the star moves relative to the others
Stable	neither of the above

The ensemble as a whole is then reported as insufficient data while any comparison is still unassessed, not ready while fewer than three comparisons are stable, and live-preview consistent otherwise.

The report is written to photometry_quality.json in the session folder and shown live in the Comparison quality panel, with the criteria that produced it recorded alongside the verdicts.

Warning

“Stable” means only that the live preview has enough internally consistent samples. It is not a calibrated-photometry certification. Confirm the ensemble on registered, calibrated frames in Siril and star_var_script.

7. Time and airmass¶

Implemented in argos.core.photometry.airmass.

The timestamp of a measurement is the exposure midpoint, converted to Julian date with the Fliegel–Van Flandern day number:

\[ \text{JD} = \text{JDN} + \frac{h - 12}{24} + \frac{\text{min}}{1440} + \frac{s}{86400} \]

BJD_TDB — the publishable time standard, applying the barycentric light-travel-time correction for the target’s direction from the observing site — is computed through astropy when the site and exposure time are available.

Tip

For transit timing and long-baseline period work, report BJD_TDB — not HJD, not JD_UTC. The difference reaches several seconds for HJD and UTC accumulates leap seconds (Eastman, Siverd & Gaudi 2010).

For an AAVSO submission, JD_UTC is what is asked for, and it is what ARGOS’s AAVSO export writes (#DATE=JD). Both columns are in photometry.csv; use the one your destination expects.

Airmass uses the Pickering (2002) formula — better than 0.01 airmass down to 1° altitude, and finite at the horizon where \(\sec z\) diverges:

\[ X = \frac{1}{\sin\!\left(h + \dfrac{244}{165 + 47\,h^{1.1}}\right)}, \qquad h \text{ in degrees} \]

It is undefined at or below the horizon — the function returns nothing rather than a large number, so a frame taken through the treetops has no airmass rather than a fictional one.

Warning

The header and the light-curve point use the same formula, but not the same input. AIRMASS in the FITS header is computed for the exposure start; the light-curve point is timed at the midpoint, and takes its airmass from the mount’s last reported altitude rather than from the target’s altitude at that midpoint. On a long exposure near the horizon the two can differ. If airmass matters to your analysis — an extinction fit, a colour-term correction — recompute it from DATE-AVG and the target coordinates rather than trusting either number.

8. What the export actually contains¶

Export measurements… writes one row per star per frame. The multi-star form prefixes star_id, role, name and auid; the rest is the same in both.

Column	Unit	Meaning
`jd_utc`	day	Julian date of the exposure midpoint, UTC
`bjd_tdb`	day	Barycentric JD in TDB — empty when the site is unknown
`mag`	mag	the differential magnitude of §4.3
`mag_err`	mag	the final uncertainty: formal and systematic combined (§5)
`formal_mag_err`	mag	the photon-only error of §3.4, before the floor
`sigma_syst`	mag	the run-level systematic floor that was added
`airmass`	—	from the mount’s altitude, at exposure start-ish (see §7)
`fwhm`	green px	frame FWHM. Multiply by 2 for full-resolution pixels, then by the plate scale for arcsec
`sky_adu`	ADU	annulus median for this star on this frame
`comps_used`	count	the flux-ratio ensemble count, not the magnitude one — see the warning below
`relative_flux`	—	\(\rho\) of §4.4, un-normalised
`relative_flux_err`	—	its propagated error
`saturated`	bool	the §3.5 saturation flag

Warning

Two traps in this file.

comps_used is not the number of comparisons behind mag. It is relative.comps_used — the count that produced \(\rho\). The two ensembles are filtered differently (the flux path also rejects suspect stars, the magnitude path does not), so the number routinely differs from the one that built the zero point in the same row.

Rows are dropped when \(\rho\) cannot be computed. A point is only emitted if the relative-flux ratio exists. If every comparison is flagged suspect, a perfectly good differential magnitude is silently absent from the curve and the export — there is no row and no note. A curve with unexplained gaps is worth checking against the frame count before you conclude the star did something.

There is no suspect column: that flag never reaches the file (§3.5).

9. The floor you cannot get under¶

Before the list of limits, one number that is not in the code and should govern your expectations. Atmospheric scintillation sets a noise floor that no exposure time and no photometric skill removes, and it scales as \(D^{-2/3}\) — punishing for a 30 mm objective. Young’s approximation,

\[ \sigma_\text{scint} \simeq 0.09\, D^{-2/3}\, X^{1.75}\, e^{-h/8000}\, (2t)^{-1/2} \]

(\(D\) in cm, \(X\) airmass, \(h\) site elevation in m, \(t\) exposure in s), evaluated for a site at 200 m:

Telescope	\(X\) = 1.0, 20 s	\(X\) = 1.5, 20 s	\(X\) = 1.5, 60 s	\(X\) = 2.0, 20 s
S30 / S30 Pro (30 mm)	7 mmag	15 mmag	8 mmag	24 mmag
S50 (50 mm)	5 mmag	10 mmag	6 mmag	17 mmag

Read that as: on a 20-second sub at airmass 1.5, an S30 Pro cannot do better than about 15 mmag per frame no matter how bright the star. Binning helps — scintillation is white on these timescales — so ten frames average to ~5 mmag. Observing high beats observing long: the \(X^{1.75}\) term costs more than the exposure term buys.

This is theory, not a measurement of your telescope. Its practical use is as a sanity check: if your measured scatter on a bright star is far below the figure above, suspect that something is smoothing your data; if it is far above, the limit is not the atmosphere and is worth chasing. Young (1967); Osborn et al. (2015) for how variable the coefficient really is from site to site.

10. Known limits in 0.4.1¶

No calibration. No dark, flat or bias. Flat-field residuals are the main reason the comparison ensemble is kept within 25 arcmin.
A cross-band zero point. \(V_\text{cat} - \text{TG}_\text{inst}\), with no colour transformation (§4.1). This is the largest systematic in the method.
An incomplete noise model. The sky-estimate term is missing, so \(\sigma_\text{formal}\) is an underestimate by ~30 % live and more offline (§3.3).
A high-frequency-only systematic floor. \(\sigma_\text{sys}\) does not contain red noise (§5), so long-baseline quantities — transit depths above all — carry error bars that are too small.
An unreconciled saturation threshold (§3.5), and flags that do less than they appear to.
Wide apertures. 30″ radius on an S30 Pro, with no deblending and no PSF fitting (§3.1).
Comparison curves are diagnostics. The check star exists to expose ensemble drift. Never submit a comparison curve as an observation.
Attended operation. There is no weather safety and no restart recovery.

What you can honestly say

The list above is long, so here is the other side of it, plainly. An ARGOS run is a legitimate detection and monitoring measurement: that a star varied, by roughly how much, with a timing you can trust to the second, against references you have evidence were stable. That is a real observation and worth recording.

What it is not is a calibrated measurement: an untransformed magnitude on an absolute scale, or a depth or amplitude quoted to a precision the error bars here can support. That comes from the reduction, on the raw frames ARGOS kept for you.

The corresponding hand-off is described in Using ARGOS — a complete session — copy the whole session folder before reducing it.

11. Every constant on this page¶

All of them are configuration keys, editable in Settings and stored in the JSON config. The defaults below are those of 0.4.1.

Key	Default	Sets
`photometry.aperture_fwhm_mult`	`2.5`	\(k\), the aperture-to-FWHM factor — §3.1
`photometry.aperture_min_px`	`4`	\(r_\text{min}\), the aperture floor in green px — §3.1
`photometry.annulus_in_px`	`8`	\(r_\text{in}\), sky annulus inner radius — §3.1
`photometry.annulus_out_px`	`12`	\(r_\text{out}\), sky annulus outer radius — §3.1
`photometry.read_noise_e`	`1.5`	\(R\), read noise in e⁻ RMS — §3.3
`camera.linearity_max_adu`	`50000`	the saturation flag threshold — §3.5
`photometry.default_band`	`TG`	the band label written to the exports — §1
`photometry.min_comparisons`	`2`	below this, a measurement is annotated, not hidden — §4.3
`photometry.auto_comparisons`	`5`	how many comparisons the automatic proposal may add — §4.5
`photometry.comparison_min_snr`	`10.0`	pilot-frame SNR gate — §4.5
`photometry.comparison_max_delta_mag`	`1.5`	instrumental-magnitude gate, in mag — §4.5
`photometry.comparison_max_separation_arcmin`	`25.0`	how far a reference may sit from the target — §4.5
`photometry.comparison_validation_min_points`	`10`	points needed before a comparison can be judged — §6
`photometry.comparison_validation_max_scatter_mag`	`0.10`	above this scatter, Unstable — §6
`photometry.comparison_validation_max_formal_error_mag`	`0.10`	above this median error, Noisy — §6
`photometry.systematic_floor_mag`	`None`	`None` derives the floor from the curve; a number imposes it — §5
`photometry.track_apertures`	`True`	whether apertures follow a fitted rigid transform between frames or are re-derived from the WCS alone
`camera.egain_table`	`{}` (empty)	\(g\) in e⁻/ADU per gain setting. Empty means the live path asks the driver, then the sensor reference — but an offline re-measurement silently uses 1.0 (§3.3)

Warning

Changing these changes what the numbers mean. Widening comparison_max_separation_arcmin buys more references at the cost of flat-field residuals; raising comparison_max_delta_mag mixes stars from different parts of the detector’s response. If you change one, record it — photometry_quality.json stores the validation criteria that were in force, but nothing stores the aperture geometry for you.